Remarks on the minimizing geodesic problem in inviscid incompressible fluid mechanics

We consider L2 minimizing geodesics along the group of volume preserving maps SDiff(D) of a given 3-dimensional domain D. The corresponding curves describe the motion of an ideal incompressible fluid inside D and are (formally) solutions of the Euler equations. It is known that there is a unique possible pressure gradient for these curves whenever their end points are fixed. In addition, this pressure field has a limited but unconditional (internal) regularity. The present paper completes these results by showing: (1) the uniqueness property can be viewed as an infinite dimensional phenomenon (related to the possibility of relaxing the corresponding minimization problem by convex optimization), which is false for finite dimensional configuration spaces such as O(3) for the motion of rigid bodies; (2) the unconditional partial regularity is necessarily limited.     

Self assembly of asymmetric tetranuclear Cu(II) [2 × 2] grid-like complexes and of a dinuclear Ni(II) complex from pyridyl-phenol Schiff base ligands

Self assembly of N-salicylidene 2-aminopyridine (L1H) with Cu(NO₃)₂·3H₂O affords [Cu₄(L1)₄(NO₃)₃(CH₃OH)][Cu(L1)(NO₃)₂](2-aminopyridinium)(NO₃)·5CH₃OH (1) which is composed of an asymmetric [2 × 2] grid-like cationic complex that co-crystallizes with a Cu(II) mononuclear anion. This remarkable tetranuclear unit presents three penta-coordinated and one hexa-coordinated Cu(II) sites. This quadruple helicate structure reveals strong anti-ferromagnetic coupling (J = −340(2) cm⁻¹) between Cu(II) ions through a double alkoxo bridge. Reacting L1H with Cu(NO₃)₂·3H₂O in slightly different conditions affords however a more symmetric tetranuclear grid-like complex: [Cu₄(L1)₄(NO₃)₂(OH)₂](2-aminopyridinium)(OH)·CH₃OH) (2). A dinuclear Ni(II) complex, [Ni₂(L2)₂(L2H)₂(NCS)₂(CH₃OH)₂]·2CH₃OH (3), obtained with another related donor ligand (L2H = N-salicylidene 3-aminomethylpyridine) was also prepared.     

Red‐NIR Luminescent Hybrid Poly(methyl methacrylate) Containing Covalently Linked Octahedral Rhenium Metallic Clusters

The embedding of functional inorganic entities into polymer matrices has become an intense field of investigation in which the main challenges are to keep the added value of the inorganic entities while preventing their self‐aggregation within the organic matrix. We present a simple way to obtain a homogeneous highly red‐NIR luminescent hybrid copolymer that contains covalently bonded nanometric‐sized {Re₆} octahedral clusters. The [Re₆Seⁱ₈(OH)^a₆]^4? cluster complexes are primarily functionalized in two steps with tert‐butylpyridine (TBP) and methacrylic acid (MAC) to give neutral [Re₆Se₈(TBP)₄(MAC)₂] building blocks that are copolymerized with methyl methacrylate (MMA) either in solution or in bulk in the presence of azobisisobutyronitrile as an initiator. Several samples containing 0, 0.025, 0.05, and 0.1 wt % of functionalized {Re₆} clusters were prepared. As the {Re₆} cluster/MMA ratio is very low, the obtained copolymers keep the entire processability of pure poly(methyl methacrylate) (PMMA), as demonstrated by differential scanning calorimetry and thermogravimetric analysis. Voltammetric and luminescence studies also indicate that the intrinsic properties of the clusters are preserved within the polymer matrix. All the samples show a bright (emission quantum yield=0.07), broad, and structureless emission band, which extends from λ=600 nm to more than λ=950 nm, with the maximum wavelength centered around λ_em=710 nm either in solution or in the solid state. Moreover, the high stability of the incorporated inorganic phosphors prevents the material from photobleaching, and thus the luminescence properties are kept entirely even after nine months of ageing.     

Inside Cover: A Synthetic Lectin for O‐Linked β‐N‐Acetylglucosamine (Angew. Chem. Int. Ed. 10/2009)

Carbohydrates are slippery customers in water. Camouflaged by solvent‐mimicking hydroxy groups, they make challenging targets, even for natural receptors. In their Communication on page 1775 ff., A. P. Davis and co‐workers describe a synthetic receptor that is remarkably effective for the important β‐N‐acetylglucosaminyl (β‐GlcNAC) unit. The affinities of the receptor are good and its selectivities are excellent, even by the standards of natural carbohydrate‐binding proteins.

     

Biomimetic surface modifications based on the cyanobacterial iron chelator anachelin

Siderophores are natural iron chelators that have been evolutionarily selected to bind to Fe ions with very high binding constants. We utilize these unique properties to bind to metal oxide surfaces using a fragment of the cyanobacterial siderophore anachelin. The resulting poly(ethylene glycol) conjugate forms stable adlayers on TiO2 as has been shown by variable angle spectroscopic ellipsometry and X-ray photoelectron spectroscopy. Moreover, these coated surfaces are highly protein-resistant against the adsorption of full human serum.     

On transfer inequalities in Diophantine approximation, II

Let Θ be a point in R ⁿ . We are concerned with the approximation to Θ by rational linear subvarieties of dimension d for 0 ≤ d ≤ n−1. To that purpose, we introduce various convex bodies in the Grassmann algebra Λ(R ⁿ⁺¹). It turns out that our convex bodies in degree d are the dth compound, in the sense of Mahler, of convex bodies in degree one. A dual formulation is also given. This approach enables us both to split and to refine the classical Khintchine transference principle.     

Functional silica nanoparticles synthesized by water-in-oil microemulsion processes

Water-in-oil (W/O) microemulsion is a well-suitable confined reacting medium for the synthesis of structured functional nanoparticles of controlled size and shape. During the last decade, it allowed the synthesis of multi-functional silica nanoparticles with morphologies as various as core–shell, homogenous dispersion or both together. The morphology and properties of the different intermediates and final materials obtained through this route are discussed in the light of UV–Vis–NIR spectroscopy, dynamic light scattering (DLS) and X-ray diffraction (XRD), transmission electron microscopy (TEM), scanning electron microscopy (SEM) and magnetometer SQUID analysis.     

Satellite Beacon Experiment for Studying Atmospheric Dynamics

To estimate the circuit quality of radio communication systems and design transmission methods for them, the designers need to quantitatively establish the way in which radio waves are transmitted within the system. Analysis of beacon data from an experiment in Nibong Tebal, Engineering Campus of Universiti Sains Malaysia (Latitude: 5.17°N and Longitude: 100.4°E) has shown evidence of diurnal, seasonal and annual variations in clear sky level. One and a half year (January 2007–June 2008) beacon data have been taken to do the analysis. This study showed the evidence of atmospheric effects to the beacon measurement.     

Structural analysis of an unusual bioactive N-acylated lipo-oligosaccharide LOS-IV in Mycobacterium marinum

Although lipo-oligosaccharides (LOSs) are recognized as major parietal components in many mycobacterial species, their involvement in the host-pathogen interactions have been scarcely documented. In particular, the biological implications arising from the high degree of structural species-specificity of these glycolipids remain largely unknown. Growing recognition of the Mycobacterium marinum-Danio rerio as a specific host-pathogen model devoted to the study of the physiopathology of mycobacterial infections prompted us to elucidate the structure-to-function relationships of the elusive end-product, LOS-IV, of the LOS biosynthetic pathway in M. marinum. Combination of physicochemical and molecular modeling methods established that LOS-IV resulted from the differential transfer on the caryophyllose-containing LOS-III of a family of very unusual N-acylated monosaccharides, naturally present as different diastereoisomers. In agreement with the partial loss of pathogenecity previously reported in a LOS-IV-deficient M. marinum mutant, we demonstrated that this terminal monosaccharide conferred to LOS-IV important biological functions, including macrophage activating properties.